Background: Amyloid fibrils are protein aggregates associated with numerous neurodegenerative diseases. Results: A theoretically consistent, two-parameter model is proposed describing very distinct amyloid fibrillization kinetics. Conclusion: Amyloid fibril formation takes place by a general mechanism involving supersaturation-dependent nucleation and growth steps. Significance: This mathematically simple model is expected to be routinely used to characterize the action of new targets for disease therapeutics.

Some of the most prevalent neurodegenerative diseases are characterized by the accumulation of amyloid fibrils in organs and tissues. Although the pathogenic role of these fibrils has not been completely established, increasing evidence suggests offpathway aggregation as a source of toxic/detoxicating deposits that still remains to be targeted. The present work is a step toward the development of off-pathway modulators using the same amyloid-specific dyes as those conventionally employed to screen amyloid inhibitors. We identified a series of kinetic signatures revealing the quantitative importance of off-pathway aggregation relative to amyloid fibrillization; these include nonlinear semilog plots of amyloid progress curves, highly variable end point signals, and half-life coordinates weakly influenced by concentration. Molecules that attenuate/intensify the magnitude of these signals are considered promising off-pathway inhibitors/promoters. An illustrative example shows that amyloid deposits of lysozyme are only the tip of an iceberg hiding a crowd of insoluble aggregates. Thoroughly validated using advanced microscopy techniques and complementary measurements of dynamic light scattering, CD, and soluble protein depletion, the new analytical tools are compatible with the high-throughput methods currently employed in drug discovery.

Amyloid fibrils and soluble oligomers are two types of protein aggregates associated with neurodegeneration. Classic therapeutic strategies try to prevent the nucleation and spread of amyloid fibrils, whilst diffusible oligomers have emerged as promising drug targets affecting downstream pathogenic processes. We developed a generic protein aggregation model and validate it against measured compositions of fibrillar and non-fibrillar assemblies of ataxin-3, a protein implicated in Machado-Joseph disease. The derived analytic rate-law equations can be used to 1) identify the presence of parallel aggregation pathways and 2) estimate the critical sizes of amyloid fibrils. The discretized population balance supporting our model is the first to quantitatively fit time-resolved measurements of size and composition of both amyloid-like and oligomeric species. The new theoretical framework can be used to screen a new class of drugs specifically targeting toxic oligomers.

A mathematical model describing the growth of crystals in impure solutions is presented. Evidence of competitive surface adsorption involving the crystallizing solute and impurities is discussed in terms of the adsorption isotherm in equilibrium and of the mechanism of occupation of active sites for growth. The impurity effect on crystal growth rates is characterized by the Langmuir adsorption constants and by the parameter β measuring the ability of the foreign species to move across the surface and occupy a stable position at the surface steps. Experimental growth rate data taken from the literature is used to test the proposed competitive adsorption model (CAM). The reported effects of the impurity concentration on the crystal growth rate at constant supersaturation are quantitatively described. Additionally, growth rate curves obtained in pure and impure solutions are used to investigate the influence of supersaturation on the relative growth rates. In all the examples considered, the CAM adequately describes the experimental data. An application example is given using the crystal growth rates of sucrose measured in a pilot evaporative crystallizer at different impurity concentrations. The kinetic effect of nonsucrose compounds existing in cane sugar solutions is characterized by estimating the average CAM parameters.